What do you mean "cut off"? Are you reaching max travels or are you getting an error that causes your solver to crash?
Flow Simulation has solution completion criteria.
In transient analysis that is generally total time.
In your case you're asking for the criteria to be when the component gets to max temperature. it doesn't know when your component will reach max temperature until you run the analysis with no criteria for stopping the calculation.
in all likelihood you will run the analysis until you see the temperature flatten out. that may be a localized maximium, it could be the absolute maximum.
But you should also compare to steady state. That will give you another reference point to understand the potential behavior of your system. But steady state won't tell you if it exceeds some value to get to steady state.